Moronic fundamentalist literalism.
So What Did Jesus Mean?
Jesus criticized Jewish leaders who love "the place of honor at feasts and the best seats in the synagogues, and salutations in the market places, and being called ‘rabbi’ by men" (Matt. 23:6–7). His admonition here is a response to the Pharisees’ proud hearts and their grasping after marks of status and prestige.
He was using hyperbole (exaggeration to make a point) to show the scribes and Pharisees how sinful and proud they were for not looking humbly to God as the source of all authority and fatherhood and teaching, and instead setting themselves up as the ultimate authorities, father figures, and teachers.
Christ used hyperbole often, for example when he declared, "If your right eye causes you to sin, pluck it out and throw it away; it is better that you lose one of your members than that your whole body be thrown into hell" (Matt. 5:29, cf. 18:9; Mark 9:47). Christ certainly did not intend this to be applied literally, for otherwise all Christians would be blind amputees! (cf. 1 John 1:8; 1 Tim. 1:15). We are all subject to "the lust of the flesh and the lust of the eyes and the pride of life" (1 John 2:16).
Since Jesus is demonstrably using hyperbole when he says not to call anyone our father—else we would not be able to refer to our earthly fathers as such—we must read his words carefully and with sensitivity to the presence of hyperbole if we wish to understand what he is saying.
Jesus is not forbidding us to call men "fathers" who actually are such—either literally or spiritually. (See below on the apostolic example of spiritual fatherhood.) To refer to such people as fathers is only to acknowledge the truth, and Jesus is not against that. He is warning people against inaccurately attributing fatherhood—or a particular kind or degree of fatherhood—to those who do not have it.
As the apostolic example shows, some individuals genuinely do have a spiritual fatherhood, meaning that they can be referred to as spiritual fathers. What must not be done is to confuse their form of spiritual paternity with that of God. Ultimately, God is our supreme protector, provider, and instructor. Correspondingly, it is wrong to view any individual other than God as having these roles.
Throughout the world, some people have been tempted to look upon religious leaders who are mere mortals as if they were an individual’s supreme source of spiritual instruction, nourishment, and protection. The tendency to turn mere men into "gurus" is worldwide.
This was also a temptation in the Jewish world of Jesus’ day, when famous rabbinical leaders, especially those who founded important schools, such as Hillel and Shammai, were highly exalted by their disciples. It is this elevation of an individual man—the formation of a "cult of personality" around him—of which Jesus is speaking when he warns against attributing to someone an undue role as master, father, or teacher.
He is not forbidding the perfunctory use of honorifics nor forbidding us to recognize that the person does have a role as a spiritual father and teacher. The example of his own apostles shows us that.